Exercises

Translate from Predicate Calculus to English, or vice versa

1. $\forall x Location(x, Antarctica) \rightarrow Temperature(x,Cold)$
   English meaning: ___________________
   
2. $\forall x Red(x) \wedge Apple(x)$
   English meaning:___________________
   
3. ___________________
   English meaning: There are some red apples
   
4. ___________________
   English meaning: All apples are red
   
5. $\exists x Apple(x) \vee Pear(x)$
   English meaning: ___________________
   
6. $Ruler(Caesar)$
   English meaning: ___________________
   
7. $\forall x Pompeian(x) \rightarrow Roman(x)$
   English meaning: ___________________
   
8. ___________________
   English meaning: All Romans were either loyal to Caesar or they hated him.
   
9. $Erupted(volcano, 79) \wedge \forall x Pompeian(x) \rightarrow Died(x,79)$
   English meaning: ___________________
   
10. $\forall x \forall t1 \forall t2 Mortal(x) \wedge Born(x,t1) \wedge GreaterThan(t2-t1,150) \rightarrow \ Dead(x,t2)$
    English meaning: ___________________
    
11. ___________________
    English meaning: All Romans who know Marcus either hate Caesar or think that anyone who hates anyone is crazy.
    
12. ___________________
    English meaning: Marcus was born in 40 A.D.